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Question

# The equation of a circle whose radius is 8 units and which touches both xâˆ’axis and yâˆ’axis is

A
x2+y216x16y+64=0
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B
x2+y2+16x16y+64=0
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C
x2+y2+16x+16y+64=0
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D
x2+y216x+16y+64=0
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Solution

## The correct options are A x2+y2−16x−16y+64=0 B x2+y2+16x−16y+64=0 C x2+y2+16x+16y+64=0 D x2+y2−16x+16y+64=0Radius of the circle =8 units. Since, the circle touches both x−axis and y−axis, the centre of the circle will be (8,8),(−8,8),(−8,−8),(8,−8). The required equation of the circle whose radius is 8 units and touches both x-axis and y-axis is (x−8)2+(y−8)2=82 ⇒x2−16x+64+y2−16y+64=64 ⇒x2+y2−16x−16y+64=0 Similarly, (x+8)2+(y−8)2=82 ⇒x2+y2+16x−16y+64=0 (x+8)2+(y+8)2=82 ⇒x2+y2+16x+16y+64=0 (x−8)2+(y+8)2=82 ⇒x2+y2−16x+16y+64=0

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